Effect of optical phonon-magnon interaction on the magnon softening at finite temperature

A magnon-phonon interaction model is set up in a two-dimensional ferromagnetic compound square-lattice system. Using the Matsubara Green function theory we calculated the magnon dispersion curves on the main symmetric line in Brillouin zone, compared the influences of the magnetic ion optical phonon with non-magnetic ion optical phonon on the magnetic excitation of the system and discussed the influences of various parameters on the magnon softening. The lower Debye temperature of ferromagnetic materials is, the more likely the magnon softening occurs. It turned out that the optical phonon-magnon coupling plays an important role on the magnon softening, the longitudinal optical phonon contributes the most to the magnon softening and magnon damping. It is also found that the contribution of the non-magnetic ion to the magnon softening and magnon damping is more significant than that of magnetic ion when the mass of the magnetic ion is less than that of the non-magnetic ion, or the mass of magnetic ion and the non-magnetic ion are equal.